On semigroup orbits of polynomials in subgroups

TL;DR

This paper investigates how the orbits generated by polynomial functions intersect with multiplicative subgroups, extending previous research to deepen understanding of polynomial dynamics in algebraic structures.

Contribution

It extends prior results on semigroup orbits and their intersections with subgroups in polynomial dynamics, providing new insights into algebraic and dynamical properties.

Findings

Extended results on intersections of polynomial orbits with subgroups

Generalized previous theorems in polynomial dynamics

Enhanced understanding of algebraic structures in dynamical systems

Abstract

We study intersections of semigroup orbits in polynomial dynamics with multiplicative subgroups, extending results of Ostafe and Shparlinski (2010).